 | 1841 - عدد الصفحات: 1316
...a factor "which makes udx + vdy + wds an exact differential, then will N (udx + vdy + to dz) = 0 be the differential equation of a surface which cuts at right angles the directions of the motion of the particles through which it passes. The proof that follows is taken from that which Mr.... | |
 | James Challis - 1875 - عدد الصفحات: 154
...calculated. Consequently, a surface conceived to be drawn in the fluid at a given instant so as to cut at right angles the directions of the motions of the particles through which it passes (which will be called a surface of displacement), must be continuous through either a finite, or an... | |
 | 1829 - عدد الصفحات: 512
...whatever, to a point at the vena contracta, the line being so drawn that it shall always be coincident with the directions of the motions of the particles through which it passes. Let therefore u = the velocity at the vena contracta, k = the section of the stream at that point,... | |
 | 1872 - عدد الصفحات: 1356
...differential, it follows that 1. is a function of 4, and t. Conceive a line to be drawn at a given instant in the directions of the motions of the particles through which it passes, and let x, y, z be the coordinates of a point the distance of which measured at the given instant along... | |
 | 1849 - عدد الصفحات: 582
...boundary in successive instants. Let now Then, as is known, \I/ = 0 is the equation of a surface cutting at right angles the directions of the motions of the particles through which it passes. The factor — is applied for the A sake of generality, because it may be assumed that such a surface... | |
 | University of Cambridge - 1838 - عدد الصفحات: 496
...the axes of .r, i/, s, at any point of a mass of fluid in motion, the equation udx + vdy 4- w dz = Q, is the differential equation of a surface which cuts at right angles the directions of motion at the points through which it passes. 14. State the reason that the Moon's apparent motion... | |
 | 1862 - عدد الصفحات: 600
...repeated here in a condensed form. Representing by s any line drawn at a given instant constantly in the directions of the motions of the particles through which it passes, and terminating at the point xys, and by V the velocity at that point, we shall have Hence, substituting... | |
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It is well known that the equation udx + vdy + wdz = 0, is the differential equation of a surface which cuts at right angles the directions of the motions of the particles through which it passes, if the left hand side of the equation be integrable per... 